# Q 13.12  From a certain apparatus, the diffusion rate of hydrogen has an average value of $28.7cm^{3}s^{-1}$ . The diffusion of another gas under the same conditions is measured to have an average rate of $7.2cm^{3}s^{-1}$. Identify the gas.

As per Graham's Law of diffusion if two gases of Molar Mass M1 and M2 diffuse with rates R1 and R2 respectively their diffusion rates are related by the following equation

$\frac{R_{1}}{R_{2}}=\sqrt{\frac{M_{2}}{M_{1}}}$

In the given question

R1 = 28.7 cm3 s-1

R2 = 7.2 cm3 s-1

M1 = 2 g

$\\M_{2}=M_{1}\left ( \frac{R_{1}}{R_{2}} \right )^{2}\\ M_{2}=2\times \left ( \frac{28.7}{7.2} \right )^{2}\\ M_{2}=31.78g$

The above Molar Mass is close to 32, therefore, the gas is Oxygen.

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